1st Year Statistics MCQs

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• 1. A variable that can take only isolated points on a number line is:
• (A) discrete variable    (B) continuous variable    (C) qualitative variable    (D) attribute
• 2. A relative frequency is expressed in the form of: (A) whole number (B) percentage (C) fractional (D) constant
• 3. The total angle in pie-diagram is: (A) 360° (B) 180° (C) 270° (D) 100°
• 4. The mean and median of any two values are always:
• (A) mean = median      (B) mean> median    (C) mean < median    (D) less than zero
• 5. Harmonic mean cannot be computed if any of the observations is: (A) one (B) negative (C) zero (D) fractional
• 6. If "X" and "Y" are independent variables then var (x - y) is equal to: 
• (A) var (X)-var (Y)      (B) var (X) + var (Y)       (C) var (X)        (D) var (Y)
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• 7. Second moment about mean is also: (A) variance (B) standard deviation (C) mean (D) median
• 8. The range of the values -2, -3, -5, -10 is: (A) -12  (B) -8  (C) 8  (D) 9
• 9- The index number of base period is always: (A) zero (B) 100  (C) greater than 100  (D) less than 100
• 10. Paasche's price index number is also known as:
• (A) current year weighted      (B) base year weighted    (C) CPI       (D) simple price index
• 11. The probability of an event is always:
• (A) greater than zero    (B) greater than one    (C) between zero and one    (D) less than zero
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• 12. The joint probability of two independent events A and B is:
• (A) P(A)+P(B)        (B) P(A)+P(B)-P(ΑΠΒ)           (C) P(A)P(A/B)         (D) P(A)P(B)
• 13. Let "x" is a random variable, then var(x) is: (A) E(x²)-(E(x))²  (B) E(x)-E(x²)  (C) E(x²)-E(x)  (D) (E(x))²-E(x²)
• 14. Let "a" is a constant and " x " is a random variable, then SD(ax) is: (A) a²SD(x)  (C) SD(x)  (B) a SD(x)  (D) zero
• 15. The standard deviation of binomial probability distribution is:  (A) np  (B) npq  (C) √npq  (D) nq
• 16. The number of parameters of binomial distribution are:  (A) 2   (B) 3   (C) 1   (D) 4
• 17. The mean of hypergeometric distribution is:  (A) NK /n (B) nK/N  (C) N/nK  (D) n/NK
• 1. Height of a plant is variable. (a) Qualitative (b) Discrete (c) Continuous (d) Attribute
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• 2. In histogram, along x-axis we take: (a) Mid points (b) Frequency (c) Cumulative frequency (d) Class boundaries
• 3. Part of the table containing row captions are called: (a) Stub (b) Box heads (c) Body (d) Foot notes
• 4. Σ(y - y)² =  (a) Least (b) Maximum (c) 0 (d) 
• 5. For averaging percentages, the useful average is: (a) Arithmetic mean (b) Median (c) Mode (d) Geometric mean
• 6. For positively skewed distribution: (a) Mean > median (b) Mean < median (c) Mean < mode (d) Median < mode
• 8. Var (ay) = (a) a Var (y) (b) a2 Var (y) (c) | a | Var (y) (d) 1/a Var (y) 
• 9. Second moment about mean is: (a) 0 (b) Mean (c) Variance (d) SD
• 10. In price relatives, the given year price is divided by the price of: (a) First year (b) Last year (c) Preceding year (d) Base year
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• 11. Fisher's index number is of the Laspeyer's and Paasche's index number. (a) AM (b) GM (c) HM (d) Median
• 12. If A and B are independent events then P(ΑΠΒ) = : (a) 0 (b) 1 (c) P(A)P(B) (d) P(A) P(B/A)
• 13. If a coin is tossed four times, the number of total sample points will be: (a) 4 (b) 8 (c) 16 (d) 2
• 14. If d and b are constant and y is a random variable, then E(by + d) = (a) bE (y) + d (b) bE (y) (c) E (y) + d (d) E (y)
• 15. If x is a random variable then Var(x)=: (a) E[x-E(x)] (b) E[x²-E(x)] (c) E[x-E(x)] (d) E [x²-(E(x))²]
• 16. Parameters of binomial distribution are: (a) n and q (b) n and p (c) pand q (d) n, p and q
• 17.Variance of hyper-geometric distribution is: (a) nN/k (b) Nk/n N-1/N-n (c) N/nk N-n/N-1 (d) (nk/N)(N-k/N)(N-n/N-1)
• 2. Write short answers to any EIGHT questions.
• i. Define statistics as a field of study.
• ii. Write any two sources of secondary data.
• iii. Define an average.
• iv. What do you mean by weighted mean?
• v. If n₁=30, n₂ = 20 and X₁ =10, X₂ =15, then find combined mean X.
• vi. Write the names of positional averages.
• vii. If sigma(x-35) = 0, sigma(x−40) = 5 and sigma(x-45)=-5 what is the value of mean and why?
• viii. What is base period?
• ix Find Paasche's price index number if 2p,q₁ = 1050 and Epoq₁ = 1000.
• x Define composite index number.
• xi Which averages are used in construction of an index number?
• xii - Find consumer's price index number by family budget method if EWI =131950 and 2po40 = 750.
• 3. Write short answers to any EIGHT questions.
• i. Define tabulation.
• ii. For the class intervals 4-7, 8-11, 12-15 make class boundaries.
• iii. Define mean deviation.
• iv. Find range of -1, -3, 0, 2, 5, 8.
• v. If Q1 = 12, Q3 = 36, find quartile deviation.
• vi. Define co-efficient of variation.
• vii. Define kurtosis.
• viii. Define simple and compound events.
• ix. What is the classical definition of probability?
• x. If A and B are independent events, P(A)=0.4, P(B) = 0.3 Find P(ΑΠΒ).
• xi. Define equally likely events.
• xii. If P(A)=0.3, P(B) = 0.8, P(A∩B) = 0.2 Find P(AUB).
• 4. Write short answers to any SIX questions.
• i. Define continuous random variable.
• ii. Define discrete probability distribution.
• iii. What are random numbers, how the random numbers can be generated?
• iv. Explain the "Mathematical Expectation".
• v. If E(x)=1.15 and E(x) = 2.15 then find var(x).
• vi. Define binomial probability distribution.
• vii. If x-b(20,3/5). Find mean and variance of binomial distribution.
• viii. Write down four properties of hypergeometric experiment.
• ix. If N=6, n=4, K3. Write down function of hypergeometric distribution. Also find P (x = 1).
• 5. (a) The daily wages for a group of 200 persons have been obtained from a frequency distribution of a continuous variable x, after making the substitution u = x-130/20.
• (b) The average wage of 4 men is Rs.17 per hour. What is the average wage of further 6 men if the average wage of all 10 men is Rs.20?
• (b) Computer calculated mean and standard deviation from 20 observations as 42 and 5  respectively. It was later discovered at the time of checking that it had copied down two values as 45 and 38 where as the correct values were 35 and 58 respectively. Find correct value of co-efficient of variation.
• (b) If two persons "A" and "B" can solve 70% and 80% of problems of a certain book respectively, then find the probability that a problem chosen at random will be solved by at least one of them.
• 9. (a) A certain event is believed to follow the binomial distribution. In Find complete binomial frequency distribution. 1024 samples of 5, p = 1/3.
• (b) There are seven people who work in an office. Of them, four would like to be transferred. If three people from this office are randomly selected for transfer, what is the probability that
• (i) All three will want to be transferred.
• (ii) At most one will want to be transferred.